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When will the boy be 2 meters from the trampoline? ___ seconds

When will the boy land on the trampoline?___ seconds

(round all answers to 2 decimal places)

Answer:

$3.30

Step-by-step explanation:

Shirt price * city sales tax = sales tax amount on shirt. $39.95 * 0.0825 = $3.30

Answer:

the new surface Will be 1/4 pf the old surface

Step-by-step explanation:

because the surface with 7 in Is about 294 and with 3.5 (1/2 of 7) Is 73.5.

so 294:4 Is 73.5

excuse me for my bad English but I'm italian

Answer:

factors

Step-by-step explanation:

To find the roots of a polynomial, it is often useful to find the Factors of the polynomial.

Using the graphical methods [online graph calculator], the domain of (fx) = (x-3)/7x is given as All real numbers except 7/2 and 0.

(−∞,0)∪(0,7/2)∪(7/2,∞),

{x∣∣x∣≠0,7/2}

A relation's domain and range are defined as the sets of all the x-coordinates and all the y-coordinates of ordered pairs, respectively.

here, we have,

y=(x^2+7x+12)/(2x^2-7x)

by solving, we get, domain as,

(−∞,0)∪(0,7/2)∪(7/2,∞),

{x∣∣x∣≠0,7/2}

Graphs may also be used to determine the domain and range of functions. The domain of a graph consists of all the input values represented on the x-axis since the domain refers to the set of potential input values. The range is the collection of potential output values represented on the y-axis.

Notice as indicated in the graph that the coordinates or ordered pairs plotted DO NOT go through the origin which is zero. Also notice that the curved lines, extend to all real numbers on the grapy to infinity.

Hence stated as a mathematical expression, the domain would be:

a domain of all real numbers except 7/2 and 0

(−∞,0)∪(0,7/2)∪(7/2,∞),

{x∣∣x∣≠0,7/2}

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The area of trapezoid ABCD is 18.5 square units.

To find the area of trapezoid ABCD, we need to use the formula for the area of a trapezoid which is: Area = (sum of the bases/2) x height. Since AB and CD are parallel, we can consider them as the two bases of the trapezoid. Let's denote the length of AB as a and the length of CD as b.

We know that the area of 4PAB is 16 square units, which means that the height of the trapezoid from point P to AB is 4 units. Similarly, we know that the area of 4PCD is 25 square units, which means that the height of the trapezoid from point P to CD is 5 units.

Now, let's consider the diagonals AC and BD. Since P is the intersection of these diagonals, we can divide the trapezoid into two triangles: APB and CPD. The sum of the areas of these two triangles is equal to the area of the trapezoid. We can use the formula for the area of a triangle which is: Area = (base x height)/2.

The base of triangle APB is a and its height is 4. Therefore, the area of APB is (a x 4)/2 = 2a. The base of triangle CPD is b and its height is 5. Therefore, the area of CPD is (b x 5)/2 = 2.5b.

The sum of the areas of APB and CPD is 2a + 2.5b = 2(a + 1.25b). This is equal to the area of the trapezoid since the sum of the areas of the two triangles is equal to the area of the trapezoid.

Therefore, the area of trapezoid ABCD is 2(a + 1.25b). Substituting the given values, we get:

Area = 2(a + 1.25b)
Area = 2(AB + 1.25CD)
Area = 2(a + 1.25b) = 2(4 + 1.25(5)) = 18.5 square units

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We have 2 points in the graph (3,4) and (-3,0) so the slope is

so the answer is A) 2/3

Based on the given equation of b -4/6=b/2, the value of the variable b, can be found to be -2

The variable can be found by solving the equation through the operations of mathematics.

First, cross-multiply:

b -4/6 = b/2

b - 4 = 6b / 2

After cross-multiplying, collect like terms:

b - 4 = 3b

b - 3b = 4

-2b = 4

b = 4 / -2

b = -2

In conclusion, the variable is -2.

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Step-by-step explanation:

The perimeter is 26 units

Answer:

               \(\dfrac1{126}\)

Step-by-step explanation:

9 all possible digits (1, 2, 3, 3, 4, 5, 6, 7, 8, 9)

4 digits and no digits repeated so

9•8•7•6      - number of all possible codes

4 even digits (2, 4, 6, 8)

4 digits and no digits repeated so

4•3•2•1       - number of all codes wich consists of all even digits

What is the probability that the lock code consists of all even didgit:

\(\dfrac{4\cdot3\cdot2\cdot1}{9\cdot8\cdot7\cdot6}=\dfrac{1\cdot1\cdot1\cdot1}{9\cdot2\cdot7\cdot1}=\dfrac1{126}\)

Answer:

8/11

Step-by-step explanation:

In the given scenario was cannot calculate P(B) directly. As it depends on what happened first, by itself we don’t know what was drawn first. Thus it becomes a conditional probability question:

P( B | A ) ← reads as the probability of “B” happening “given that” “A” has already happened — in this case the probability that the second marble drawn is a blue marble given that the first was a red marble.

Answer:

B

Step-by-step explanation:

I think the answer is b because each space of the shelf can hold 1 of 8 different books and there are 6 different spots so it would be 8x6 which equals 48. I hope this makes sence and helps.

Answer:

hmmm really interested but hard to get

and not easy

Answer:

{− 4 1/2,  −3/4, 0}

Step-by-step explanation:

Answer:

DE

Step-by-step explanation:

........................

Answer:  \(\sqrt{13}\) units

Work Shown:

\((x_1,y_1) = (-5,-4) \text{ and } (x_2, y_2) = (-2,-6)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-5-(-2))^2 + (-4-(-6))^2}\\\\d = \sqrt{(-5+2)^2 + (-4+6)^2}\\\\d = \sqrt{(-3)^2 + (2)^2}\\\\d = \sqrt{9 + 4}\\\\d = \sqrt{13}\\\\d \approx 3.6056\\\\\)

I used the distance formula.

A slightly alternate method is to form a right triangle and use the pythagorean theorem. The hypotenuse will have the endpoints (-5,-4) and (-2,-6).

Answer:

c) $ 12.00

Step-by-step explanation:

$78.20 x 15%= 11.75

round up

The longest possible integer length of the third side of the triangle is 6 < x < 28

The sum of any two sides must be greater than the third side for a triangle to exist

let the third side be x

x + 11 > 17 and x + 17 > 11 and 11 + 17 > x

x > 6 and x > - 6 and x < 28

The longest possible integer length of the third side of the triangle is 6 < x < 28

The length of the 3 sides of a triangle needs to always be among (however no longer the same) the sum and the difference of the opposite two sides. As an example, take the instance of two, 6, and seven. and. consequently, the third side period should be extra than 4 and less than 8.

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Answer:

27

Step-by-step explanation:

Let the third side length be s. Then, by the Triangle Inequality, we know that s satisfies the inequalities

\(s + 11 & > 17, \\ s + 17 & > 11, \\ 11 + 17 & > s.\)

\(\begin{align*} s + 11 & > 17, \\ s + 17 & > 11, \\ 11 + 17 & > s.\end{align*}\)

The first two inequalities hold as long as s > 6 and the third holds if s < 28. The largest possible integer s that satisfies all of these is 27.

Answer:

24

Step-by-step explanation:

Okay, let's solve this step-by-step:

1) We are given: a = -8, b = 2, c = 7, d = 11

2) We are asked to solve the matrix equation: [[x + y, z], [z - x, w - y]] = [[a, b], [c, d]]

3) Matching up the elements in the matrices:

x + y = a = -8 (1)

z = b = 2 (2)

z - x = c = 7 (3)

w - y = d = 11 (4)

4) Solving the equations:

From (1): x + y = -8 => x = -8 - y

Substitute in (3): z - (-8 - y) = 7 => z - (-8) = 7 + y => z = 15 + y

Substitute (2) into the above: 2 = 15 + y => y = 13

Substitute y = 13 into (1): -8 - 13 = -21 = x

Substitute x = -21 and y = 13 into (4): w - 13 = 11 => w = 11 + 13 = 24

Therefore, the values are:

x = -21

y = 13

z = 15

w = 24

So the final value of w is:

w = 24

Answer:

A

Step-by-step explanation:

Answer:

100 degrees

Step-by-step explanation:

You can tell by just looking at the picture :)

The correct simplification would be \(18x^4 - 36x^3 + 9x^2\) (option a).

To simplify the expression \(9x^2(4x - 2x^2\) - 1), we need to perform the multiplication and combine like terms.

1. Start by distributing the 9x^2 to each term inside the parentheses:

  \(9x^2 * 4x = 36x^3 9x^2 * (-2x^2) = -18x^4 9x^2 * (-1) = -9x^2\)

2. Now we can combine the terms obtained from the distribution:

\(36x^3 - 18x^4 - 9x^2\)

3. Rearranging the terms in descending order of exponents:

\(-18x^4 + 36x^3 - 9x^2\)

4. However, we can simplify this expression further by factoring out a common factor of \(-9x^2\):

\(-9x^2(2x^2 - 4x + 1)\)

5. Thus, the final simplified expression is:

\(18x^4 - 36x^3 + 9x^2\)

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To classify the quadratic surface S, we need to analyze its equation.

The equation of S is given by 2x^2 + y^2 - 2z^2 = 10.

(a) To classify S:

We observe that the coefficients of x^2, y^2, and z^2 have different signs.

This indicates that S is a hyperboloid of two sheets.

(b) To find the upward-pointing unit normal N to S at (2, 2, 1):

To determine the unit normal vector at a point on the surface, we take the gradient of the equation of S and normalize it.

The gradient of S is given by ∇S = (∂S/∂x)i + (∂S/∂y)j + (∂S/∂z)k.

Taking partial derivatives of S with respect to each variable, we have:

∂S/∂x = 4x

∂S/∂y = 2y

∂S/∂z = -4z

At the point (2, 2, 1), the gradient becomes:

∇S = (4(2))i + (2(2))j + (-4(1))k

= 8i + 4j - 4k

To obtain the unit normal, we normalize ∇S:

N = (∇S) / ||∇S||

Calculating the magnitude of ∇S:

||∇S|| = √(8^2 + 4^2 + (-4)^2)

= √(64 + 16 + 16)

= √96

= 4√6

Dividing ∇S by ||∇S||, we get:

N = (8i + 4j - 4k) / (4√6)

= (2i + j - k) / √6

Therefore, the upward-pointing unit normal N to S at (2, 2, 1) is (2i + j - k) / √6.

(c) To find an equation of the tangent plane P to S at the point (2, 2, 1):

The equation of a plane can be given in the form Ax + By + Cz + D = 0, where (A, B, C) is the normal vector to the plane.

We already have the normal vector N = (2i + j - k) / √6 from part (b). Now, to find D, we substitute the coordinates (2, 2, 1) into the plane equation:

A(2) + B(2) + C(1) + D = 0

Substituting the components of N, we get:

(2)(2) + (1)(2) + (-1)(1) + D = 0

4 + 2 - 1 + D = 0

D = -5

Therefore, an equation for the tangent plane P to S at the point (2, 2, 1) is:

2x + y - z - 5 = 0.

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Answer:

4

Step-by-step explanation:

Answer:

La respuesta seria 3 espero que esto ayude

Step-by-step explanation:

Answer: 7a

Step-by-step explanation:

Step-by-step explanation:

do sum of 3a and 4a your answer will be 7a

She has to find if the tree is tall enough to fall into her house.

She is using a 12-inches ruler to find proportions. We can draw this as:

The triangle that can be drawn using as vertices the base of the tree, the top of the tree and the house is similar to the triangle formed by the rule and the the distance of 1 ft.

We can see that as the height of the ruler that indicates the top of the tree is smaller than the foot, we know that the height H of the tree is smaller than the distance D from the house to the tree, in the same proportion.

We can calculate the height of the tree using the following proportion:

Answer: The house is far enough, as the height of the tree is less than 50 ft (it is 37.5 ft)

The probability that fewer than four customers will arrive in a 30-minute segment is 0.0483, rounded to four decimal places.

Based on the given information, we know that the arrivals to the ATM follow a Poisson distribution with a mean of 4 per 15 minutes.

a. To determine the probability that three customers will arrive in a given 15-minute segment, we can use the Poisson probability formula:

P(X = 3) = (e^-4) * (4^3) / 3!

Where X is the number of arrivals, e is the mathematical constant approximately equal to 2.71828, and 3! means 3 factorial, which is 3 * 2 * 1 = 6.

Plugging in the values, we get:

P(X = 3) = (e^-4) * (4^3) / 3! = 0.1954

So the probability that three customers will arrive in a given 15-minute segment is 0.1954, rounded to four decimal places.

b. To find the probability that fewer than four customers will arrive in a 30-minute segment, we need to use the Poisson distribution again, but this time with a mean of 8 (since there are two 15-minute segments in 30 minutes, and the mean for one segment is 4).

We want to find P(X < 4) or P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3).

Using the Poisson probability formula with a mean of 8:

P(X = 0) = e^-8 * (8^0) / 0! = 0.0003
P(X = 1) = e^-8 * (8^1) / 1! = 0.0030
P(X = 2) = e^-8 * (8^2) / 2! = 0.0122
P(X = 3) = e^-8 * (8^3) / 3! = 0.0328

Adding up these probabilities, we get:

P(X < 4) = 0.0003 + 0.0030 + 0.0122 + 0.0328 = 0.0483

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Answer:

See below.

Step-by-step explanation:

A) 3

B) 11

C) 7

-hope it helps

Answer:

a) 3

b) 11

c) 7

Step-by-step explanation:

The factors of 21 are: 1, 3, 7, 21

The factors of 411 are: 1, 3, 137, 411

A common prime factor is 3.

The factors of 77 are: 1, 7, 11, 77

The factors of 242 are: 1, 2, 11, 22, 121, 242

A common prime factor is 11.

The factors of 56 are: 1, 2, 4, 7, 8, 14, 28, 56

The factors of 63 are: 1, 3, 7, 9, 21, 63

A common prime factor is 7.

Answer:

Yes, john did make his scale factor the right way, because

Step-by-step explanation:

3 x 2.5 = 7.5, Seen on the right figure/shape/parallelogram

2 x 2.5 = 5, Seen on the right figure/shape/parallelogram

Edit:

Brainliest? :)

Answer:

Yes he did it correctly

Step-by-step explanation:

Option 2 is correct that is 1.79

When presented in ascending order, the value that 75% of data points fall within is known as the higher quartile, or third quartile (Q3).

The quartiles formula is as follows:

Upper Quartile (Q3) = 3/4(N+1)

Lower Quartile (Q1) = (N+1) * 1/3

Middle Quartile (Q2) = (N+1) * 2/3

Interquartile Range = Q3 -Q1,

1.74, 0.24, 1.56, 2.79, 0.89, 1.16, 0.20, and 1.84 are available.

Sort the data as follows: 0.20, 0.24, 0.89, 1.16, 1.56, 1.74, 1.84, 2.79 in ascending order of magnitude.

The data set has 8 values.

hence, n = 8; third quartile: 3/4 (n+1)th term

Q3 =3/4 of a term (9) term

Q3 =27/4 th term

Q3 = 1.74 + 1.84 / 2 (average of the sixth and seventh terms)

equals 1.76

Thus Q3 is 1.76 that is option 2

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David can best improve his investigation by including a control group. A control group is a group that does not receive any treatment or intervention and is used as a benchmark to compare the results of the experimental group. In this case, the control group would be a third young elm tree that is planted near the other two but does not receive any water or fertilizer. David can measure the height and trunk girth of the control tree every week for a year as well.

In scientific research, it is important to include a control group to ensure that the results of the experimental group are due to the treatment or intervention and not due to other factors. In this case, David is investigating the factors that affect plant growth, and he is manipulating the amount of water and fertilizer that the two elm trees receive. However, there could be other factors that affect plant growth, such as soil quality, sunlight exposure, temperature, and pests. If David only measures the height and trunk girth of the two elm trees that receive water and fertilizer, he cannot be sure if any changes in their growth are due to the treatment or due to other factors.

To improve his investigation, David can plant a third young elm tree near the other two and not give it any water or fertilizer. This third tree will serve as the control group, and David can measure its height and trunk girth every week for a year as well. By comparing the growth of the experimental group (the two elm trees that receive water and fertilizer) to the growth of the control group (the third elm tree that receives nothing), David can be more confident that any changes in the growth of the experimental group are due to the treatment and not due to other factors.

David can best improve his investigation by including a control group, which will serve as a benchmark to compare the results of the experimental group. The control group should be a third young elm tree that is planted near the other two but does not receive any water or fertilizer. David can measure the height and trunk girth of the control tree every week for a year as well. By comparing the growth of the experimental group (the two elm trees that receive water and fertilizer) to the growth of the control group (the third elm tree that receives nothing), David can be more confident that any changes in the growth of the experimental group are due to the treatment and not due to other factors.

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